Can you record a conversation between you and your attorney?

This answer should not be considered specific legal advice, nor does it establish an attorney client relationship. Generally, under the scenario you propose, you can only record a conversation with the permission of all parties to the conversation, or it is a crime.

In addition to Mr. Woodring's answer, I would say that recording the conversation may remove one of the main benefits of the attorney-client relationship: confidentiality. Once you waive the privilege of confidentiality by recording and letting another listen to the recording, you may also have to let out information you do not intend to be let out. So think that through carefully before committing to a course of action.